Phantom chain simulations for fracture of star polymer networks on the effect of arm molecular weight

This study investigated the fracture of star polymer networks made from prepolymers with various arm molecular weights in the range $2\le N_a\le 0$, for node functionalities $3\le f\le 8$ and conversion ratios $0.6\le {\phi }_c\le 0.95$ by phantom chain simulations. The networks were created via end-linking reactions of star polymers dispersed in a simulation box with a fixed monomer density $\rho =8$. The resultant networks were alternatively subjected to energy minimization and uniaxial stretch until the break. The stretch at the break, ${\lambda }_b$, depended on the strand molecular weight $N_s=2N_a+1$ with a power-law manner described as ${\lambda }_b\sim N_s^0.67$, consistent with the experiment. However, the strand length before stretch is proportional to $N_s^0.5$, which does not explain the observed N_s-dependence of ${\lambda }_b$. The analysis based on the non-affine deformation theory does not interpret the phenomenon either. Instead, the increase of normalized prepolymer concentration concerning the overlapping concentration with increasing $N_s$ explains the result through a rise in the fraction of broken strands.